Package org.hipparchus.analysis.polynomials

Class PolynomialFunction

java.lang.Object

org.hipparchus.analysis.polynomials.PolynomialFunction

All Implemented Interfaces:

Serializable, UnivariateDifferentiableFunction, FieldUnivariateFunction, UnivariateFunction

public class PolynomialFunction
extends Object
implements UnivariateDifferentiableFunction, FieldUnivariateFunction, Serializable

Immutable representation of a real polynomial function with real coefficients.

Horner's Method is used to evaluate the function.

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	PolynomialFunction.Parametric	Dedicated parametric polynomial class.

Constructor Summary

Constructors

Constructor	Description
PolynomialFunction(double[] c)	Construct a polynomial with the given coefficients.

Method Summary

Modifier and Type	Method	Description
PolynomialFunction	add(PolynomialFunction p)	Add a polynomial to the instance.
PolynomialFunction	antiDerivative()	Returns an anti-derivative of this polynomial, with 0 constant term.
int	degree()	Returns the degree of the polynomial.
protected static double[]	differentiate(double[] coefficients)	Returns the coefficients of the derivative of the polynomial with the given coefficients.
boolean	equals(Object obj)
protected static double	evaluate(double[] coefficients, double argument)	Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument.
double[]	getCoefficients()	Returns a copy of the coefficients array.
int	hashCode()
double	integrate(double lower, double upper)	Returns the definite integral of this polymomial over the given interval.
PolynomialFunction	multiply(PolynomialFunction p)	Multiply the instance by a polynomial.
PolynomialFunction	negate()	Negate the instance.
PolynomialFunction	polynomialDerivative()	Returns the derivative as a PolynomialFunction.
PolynomialFunction	subtract(PolynomialFunction p)	Subtract a polynomial from the instance.
String	toString()	Returns a string representation of the polynomial.
double	value(double x)	Compute the value of the function for the given argument.
DerivativeStructure	value(DerivativeStructure t)	Simple mathematical function.
<T extends RealFieldElement<T>> T	value(T t)	Compute the value of the function.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.hipparchus.analysis.FieldUnivariateFunction

toRealFieldUnivariateFunction

Constructor Detail

PolynomialFunction

public PolynomialFunction(double[] c)
                   throws MathIllegalArgumentException,
                          NullArgumentException

Construct a polynomial with the given coefficients. The first element of the coefficients array is the constant term. Higher degree coefficients follow in sequence. The degree of the resulting polynomial is the index of the last non-null element of the array, or 0 if all elements are null.

The constructor makes a copy of the input array and assigns the copy to the coefficients property.

Parameters:

c - Polynomial coefficients.

Throws:

NullArgumentException - if c is null.

MathIllegalArgumentException - if c is empty.

Method Detail

value

public double value(double x)

Compute the value of the function for the given argument.

The value returned is

coefficients[n] * x^n + ... + coefficients[1] * x + coefficients[0]

Specified by:

value in interface UnivariateFunction

Parameters:

x - Argument for which the function value should be computed.

Returns:

the value of the polynomial at the given point.

See Also:

UnivariateFunction.value(double)

degree

public int degree()

Returns the degree of the polynomial.

Returns:

the degree of the polynomial.

getCoefficients

public double[] getCoefficients()

Returns a copy of the coefficients array.

Changes made to the returned copy will not affect the coefficients of the polynomial.

Returns:

a fresh copy of the coefficients array.

evaluate

protected static double evaluate(double[] coefficients,
                                 double argument)
                          throws MathIllegalArgumentException,
                                 NullArgumentException

Uses Horner's Method to evaluate the polynomial with the given coefficients at the argument.

Parameters:

coefficients - Coefficients of the polynomial to evaluate.

argument - Input value.

Returns:

the value of the polynomial.

Throws:

MathIllegalArgumentException - if coefficients is empty.

NullArgumentException - if coefficients is null.

value

public DerivativeStructure value(DerivativeStructure t)
                          throws MathIllegalArgumentException,
                                 NullArgumentException

Simple mathematical function.

UnivariateDifferentiableFunction classes compute both the value and the first derivative of the function.

Specified by:

value in interface UnivariateDifferentiableFunction

Parameters:

t - function input value

Returns:

function result

Throws:

MathIllegalArgumentException - if coefficients is empty.

NullArgumentException - if coefficients is null.

value

public <T extends RealFieldElement<T>> T value(T t)
                                        throws MathIllegalArgumentException,
                                               NullArgumentException

Compute the value of the function.

Specified by:

value in interface FieldUnivariateFunction

Type Parameters:

T - the type of the field elements

Parameters:

t - Point at which the function value should be computed.

Returns:

the value of the function.

Throws:

MathIllegalArgumentException - if coefficients is empty.

NullArgumentException - if coefficients is null.

Since:

1.3

add

public PolynomialFunction add(PolynomialFunction p)

Add a polynomial to the instance.

Parameters:

p - Polynomial to add.

Returns:

a new polynomial which is the sum of the instance and p.

subtract

public PolynomialFunction subtract(PolynomialFunction p)

Subtract a polynomial from the instance.

Parameters:

p - Polynomial to subtract.

Returns:

a new polynomial which is the instance minus p.

negate

public PolynomialFunction negate()

Negate the instance.

Returns:

a new polynomial with all coefficients negated

multiply

public PolynomialFunction multiply(PolynomialFunction p)

Multiply the instance by a polynomial.

Parameters:

p - Polynomial to multiply by.

Returns:

a new polynomial equal to this times p

differentiate

protected static double[] differentiate(double[] coefficients)
                                 throws MathIllegalArgumentException,
                                        NullArgumentException

Returns the coefficients of the derivative of the polynomial with the given coefficients.

Parameters:

coefficients - Coefficients of the polynomial to differentiate.

Returns:

the coefficients of the derivative or null if coefficients has length 1.

Throws:

MathIllegalArgumentException - if coefficients is empty.

NullArgumentException - if coefficients is null.

antiDerivative

public PolynomialFunction antiDerivative()

Returns an anti-derivative of this polynomial, with 0 constant term.

Returns:

a polynomial whose derivative has the same coefficients as this polynomial

integrate

public double integrate(double lower,
                        double upper)

Returns the definite integral of this polymomial over the given interval.

[lower, upper] must describe a finite interval (neither can be infinite and lower must be less than or equal to upper).

Parameters:

lower - lower bound for the integration

upper - upper bound for the integration

Returns:

the integral of this polymomial over the given interval

Throws:

MathIllegalArgumentException - if the bounds do not describe a finite interval

polynomialDerivative

public PolynomialFunction polynomialDerivative()

Returns the derivative as a PolynomialFunction.

Returns:

the derivative polynomial.

toString

public String toString()

Returns a string representation of the polynomial.

The representation is user oriented. Terms are displayed lowest degrees first. The multiplications signs, coefficients equals to one and null terms are not displayed (except if the polynomial is 0, in which case the 0 constant term is displayed). Addition of terms with negative coefficients are replaced by subtraction of terms with positive coefficients except for the first displayed term (i.e. we display -3 for a constant negative polynomial, but 1 - 3 x + x^2 if the negative coefficient is not the first one displayed).

Overrides:

toString in class Object

Returns:

a string representation of the polynomial.

hashCode

public int hashCode()

Overrides:

hashCode in class Object

equals

public boolean equals(Object obj)

Overrides:

equals in class Object